# There are 200 mg of a radioactive substance in a sample. The sample decreases by 7.85% each day. To the nearest hundredth, how many mg of the substance remain after 3 days have elapsed?

embizze | Certified Educator

We are given an initial amount of 200mg and a decay rate of 7.85% per day. We are asked to find the amount remaining after 3 days:

The general formula for exponential decay is `A(t)=P(1-r)^t` where r is the decay rate (1-r is the decay factor), P is the inital amount, and t is the time.

`A(3)=200(1-.0785)^3~~156.5006027`

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To the nearest hundredth, there are 156.50mg remaining.

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You can check by doing all three days manually:

7.85% of 200 is 15.7, so after 1 day there are 200-15.7=184.3mg

7.85% of 184.3 is 14.46755, so after 2 days there are 184.3-14.46755=169.83245mg

7.85% of 169.83245 is 13.33184733, so after 3 days there are 169.83245-13.33184733=156.5006027mg remaining.